President Barack Obama signed an executive order Monday banning federal contractors from discriminating against employees on the basis of sexual orientation or gender identity .

Despite calls from religious leaders , faith-based groups will not be exempt .

`` Thanks to your passion and advocacy and the irrefutable rightness of your cause , our government -- a government of the people , by the people and for the people -- will become just a little bit fairer , '' Obama said .

Gay federal workers are already protected from workplace discrimination by a Clinton-era order and Obama 's action extended the protections to shield workers from gender identity-based discrimination .

Americans United for Separation of Church and State , which joined a coalition of nearly 100 civil rights and LGBT groups urging Obama to reject calls for a religious exemption , thanked him for taking action . It said he made the `` right call '' for not tagging any religious exemptions to the document .

`` Faith-based groups that tap the public purse should play by the same rules as everyone else and not expect special treatment , '' the group 's executive director , Rev. Barry Lynn , said in a statement . `` No forms of discrimination should be supported with the taxpayer dime , period . ''

Rea Carey , executive director of the National Gay and Lesbian Task Force , was in the room as Obama signed the order and said it was an emotional moment .

`` There are now millions of LGBT people and their families who are just going to sleep a little bit easier tonight knowing that they ca n't be fired from their jobs as federal contractors , '' she said .

During the ceremony , which comes 50 years after President Lyndon Johnson signed the Civil Rights Act of 1964 , Obama also recalled the history of executive actions and legislation to ban discrimination in the workplace and `` make sure we the people applies to all the people . ''

Senate passes LGBT anti-discrimination bill

But Obama 's signature on Monday did not touch a 2002 executive order signed by President George W. Bush that allows religious groups to weigh prospective employees ' faith in hiring decisions .

This gave some opponents of the order hope that they could continue to consider sexual orientation in hiring decisions .

One of those opponents , Stephen Schneck , director of the Institute for Policy Research & Catholic Studies at The Catholic University of America , said he was disappointed by Obama 's decision regarding the religious exemption . But he suggested that religious groups could still rely on the 2002 order .

`` I believe the administration has left open a path that religious groups can work with , '' Schneck said .

Russell Moore , president of the Ethics & Religious Liberty Commission of the Southern Baptist Convention , had stronger words for Obama and worried that the Bush-era executive order would leave out some faith-based groups .

`` While we do n't know the full implications of this executive order , I am disappointed that this administration persistently violates the freedom of conscience for religious organizations that provide necessary relief for the poor and endangered , '' Moore said . `` The ones hurt will be the most vulnerable in our society . ''

Obama 's executive action extends protections against sexual-based discrimination to employees of federal contractors operating outside of the 21 states and the District of Columbia that enacted their own non-discrimination legislation .

Obama also noted that a majority of Fortune 500 companies have policies in place against discrimination based on sexual orientation .

The action is not the first time Obama has used his presidential powers to benefit the LGBT community . In 2010 , he signed an order extending benefits to same-sex partners of executive branch employees already provided to opposite-sex partners .

But on the federal legislative level , LGBT groups have struggled to enact similar legislation .

The Senate passed a bill barring LGBT discrimination in the fall . But the measure , which exempted religious groups from the would-be-law , did not make it to the House floor where Republicans opposed it .

And attendees greeted Obama 's call to continue applying pressure to `` resolve this problem once and for all '' with one resounding word : `` Amen . ''

Supreme Court rules against Obama in contraception case

@highlight

Executive order bars contractors covers LGBT employees ; Religious groups not exempt

@highlight

It did not touch a previous order allowing religious groups to weigh faith in hiring decisions

@highlight

Opponents disappointed on decision involving religious groups